Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?lasda

Computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal
d
 and off-diagonal
e
. Used by
?bdsdc
.

Syntax

void slasda
(
lapack_int
*icompq
,
lapack_int
*smlsiz
,
lapack_int
*n
,
lapack_int
*sqre
,
float
*d
,
float
*e
,
float
*u
,
lapack_int
*ldu
,
float
*vt
,
lapack_int
*k
,
float
*difl
,
float
*difr
,
float
*z
,
float
*poles
,
lapack_int
*givptr
,
lapack_int
*givcol
,
lapack_int
*ldgcol
,
lapack_int
*perm
,
float
*givnum
,
float
*c
,
float
*s
,
float
*work
,
lapack_int
*iwork
,
lapack_int
*info
);
void dlasda
(
lapack_int
*icompq
,
lapack_int
*smlsiz
,
lapack_int
*n
,
lapack_int
*sqre
,
double
*d
,
double
*e
,
double
*u
,
lapack_int
*ldu
,
double
*vt
,
lapack_int
*k
,
double
*difl
,
double
*difr
,
double
*z
,
double
*poles
,
lapack_int
*givptr
,
lapack_int
*givcol
,
lapack_int
*ldgcol
,
lapack_int
*perm
,
double
*givnum
,
double
*c
,
double
*s
,
double
*work
,
lapack_int
*iwork
,
lapack_int
*info
);
Include Files
  • mkl.h
Description
Using a divide and conquer approach,
?lasda
 computes the singular value decomposition (
SVD
) of a real upper bidiagonal
n
-by-
m
 matrix
B
 with diagonal
d
 and off-diagonal
e
, where
m
 =
n
 +
sqre
.
The algorithm computes the singular values in the
SVD
B
 =
U
*
S
*
VT
. The orthogonal matrices
U
 and
VT
 are optionally computed in compact form. A related subroutine
?lasd0
 computes the singular values and the singular vectors in explicit form.
Input Parameters
icompq
Specifies whether singular vectors are to be computed in compact form, as follows:
= 0: Compute singular values only.
= 1: Compute singular vectors of upper bidiagonal matrix in compact form.
smlsiz
The maximum size of the subproblems at the bottom of the computation tree.
n
The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array
d
.
sqre
Specifies the column dimension of the bidiagonal matrix.
If
sqre
 = 0
: the bidiagonal matrix has column dimension
m
 =
n
If
sqre
 = 1
: the bidiagonal matrix has column dimension
m
 =
n
 + 1
.
d
Array,
DIMENSION
 (
n
). On entry,
d
 contains the main diagonal of the bidiagonal matrix.
e
Array,
DIMENSION
 (
m
 - 1 ). Contains the subdiagonal entries of the bidiagonal matrix. On exit,
e
 is destroyed.
ldu
The leading dimension of arrays
u
,
vt
,
difl
,
difr
,
poles
,
givnum
, and
z
.
ldu
≥
n
.
ldgcol
The leading dimension of arrays
givcol
 and
perm
.
ldgcol
≥
n
.
work
Workspace array,
DIMENSION
(6
n
+(
smlsiz
+1)
2
)
.
iwork
Workspace array,
Dimension
 must be at least (7
n
).
Output Parameters
d
On exit
d
, if
info
 = 0
, contains the singular values of the bidiagonal matrix.
u
Array,
DIMENSION
 (
ldu
,
smlsiz
) if
icompq
 =1
.
Not referenced if
icompq
 = 0
.
If
icompq
 = 1
, on exit,
u
 contains the left singular vector matrices of all subproblems at the bottom level.
vt
Array,
DIMENSION
 (
ldu
,
smlsiz
+1 ) if
icompq
 = 1
, and not referenced if
icompq
 = 0
. If
icompq
 = 1
, on exit,
vt
' contains the right singular vector matrices of all subproblems at the bottom level.
k
Array,
DIMENSION
 (
n
) if
icompq
 = 1
 and
DIMENSION
 (1) if
icompq
 = 0
.
If
icompq
 = 1
, on exit,
k
(
i
) is the dimension of the
i
-th secular equation on the computation tree.
difl
REAL
 for
slasda
DOUBLE PRECISION
 for
dlasda
.
Array,
DIMENSION
 (
ldu
,
nlvl
 ),
where
nlvl
 = floor(log
2
(
n
/
smlsiz
))
.
difr
Array,
DIMENSION
 (
ldu
, 2
nlvl
 ) if
icompq
 = 1
 and
DIMENSION
 (
n
) if
icompq
 = 0
.
If
icompq
 = 1
, on exit,
difl
(1:
n
,
i
) and
difr
(1:
n
,2
i
 -1) record distances between singular values on the
i
-th level and singular values on the (
i
 -1)-th level, and
difr
(1:
n
, 2i ) contains the normalizing factors for the right singular vector matrix. See
?lasd8
 for details.
z
Array,
DIMENSION
 (
ldu
,
nlvl
 ) if
icompq
 = 1
 and
DIMENSION
 (
n
) if
icompq
 = 0
. The first
k
 elements of
z
(1,
i
) contain the components of the deflation-adjusted updating row vector for subproblems on the
i
-th level.
poles
Array,
DIMENSION
(
ldu
, 2*
nlvl
)
if
icompq
 = 1
, and not referenced if
icompq
 = 0
. If
icompq
 = 1
, on exit,
poles
(1, 2
i
 - 1) and
poles
(1, 2
i
) contain the new and old singular values involved in the secular equations on the
i
-th level.
givptr
Array,
DIMENSION
 (
n
) if
icompq
 = 1
, and not referenced if
icompq
 = 0
. If
icompq
 = 1
, on exit,
givptr
(
i
 ) records the number of Givens rotations performed on the
i
-th problem on the computation tree.
givcol
Array,
DIMENSION
(
ldgcol
, 2*
nlvl
)
 if
icompq
 = 1
, and not referenced if
icompq
 = 0
. If
icompq
 = 1
, on exit, for each
i
,
givcol
(1, 2
i
 - 1) and
givcol
(1, 2
i
) record the locations of Givens rotations performed on the
i
-th level on the computation tree.
perm
Array,
DIMENSION
 (
ldgcol
,
nlvl
 ) if
icompq
 = 1
, and not referenced if
icompq
 = 0
. If
icompq
 = 1
, on exit,
perm
 (1,
i
) records permutations done on the
i
-th level of the computation tree.
givnum
Array
DIMENSION
 (
ldu
, 2*
nlvl
 ) if
icompq
 = 1
, and not referenced if
icompq
 = 0
. If
icompq
 = 1
, on exit, for each
i
,
givnum
(1, 2
i
 - 1) and
givnum
(1, 2
i
) record the
C
- and
S
-values of Givens rotations performed on the
i
-th level on the computation tree.
c
Array,
DIMENSION
 (
n
) if
icompq
 = 1
, and
DIMENSION
 (1) if
icompq
 = 0
.
If
icompq
 = 1
 and the
i
-th subproblem is not square, on exit,
c
(
i
) contains the
C
-value of a Givens rotation related to the right null space of the
i
-th subproblem.
s
Array,
DIMENSION
 (
n
)
icompq
 = 1
, and
DIMENSION
 (1) if
icompq
 = 0
.
If
icompq
 = 1
 and the
i
-th subproblem is not square, on exit,
s
(
i
) contains the
S
-value of a Givens rotation related to the right null space of the
i
-th subproblem.
info
= 0: successful exit.
< 0: if
info
 = -
i
, the
i
-th argument had an illegal value
> 0: If
info
 = 1
, an singular value did not converge

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804